A unique feature of rotor vibration is the presence of a rotor, which by definition has to rotate, sometimes at very high speeds, to allow the machine to conduct its function. This rotation has two major implications. One implication is that a huge amount of kinetic energy is stored in the rotating machine. If a mechanism allows some of this energy to be transferred from the rotation to the rotor vibration, this would certainly lead to instability of the machine. Some mechanisms that allow this energy transfer and result in instability of rotating machines are: internal damping, aerodynamic cross coupling, seals, high speed journal bearings, intershaft squeeze film dampers, etc.
The other implication of rotation is the perpetual presence of an exciting force on the rotating machine. There is always some residual unbalance in the rotor; this residual unbalance forces the rotor at different speeds and possibly excites the critical speeds.
The presence of these two unique features of rotor vibrations: instability and unbalance excitation, result in the need to control rotor vibrations. If left uncontrolled, the unbalance excitation may result in excessive transmitted force; the critical speeds may result in excessive vibration amplitude, while instability may result in machine destruction.
Since the early work of Rankine, who suggested that machines would never be able to cross critical speeds, major strides have occurred in the development of rotor-bearing systems. Nowadays, high speed-high performance rotating machines such as gas turbines, compressors, steam turbines, turbo expanders, and turbochargers, etc., routinely cross as many as six critical speeds during their normal operating procedures.
To control the vibration of such high-speed machines, many turbomachinery manufacturers resort to either passive or active vibration control. Perhaps the first method of vibration control was the introduction of fluid film bearings in the late nineteenth century. The first application of “non-contact” journal bearings was hailed as a major breakthrough at the time, with suggestions that this should lead to the solution of all rotating machinery problems. However, soon thereafter the problems of journal bearings and fluid film bearings in general became apparent. Two basic characteristics obscured the success of fluid film bearings. One is the tendency of journal bearings to cause oil whirl and oil whip, which can be destructive instability mechanisms in rotor-bearing systems. This led to the introduction of more sophisticated fluid film bearings such as the elliptic bearing, offset-half bearing, pressure dam bearing, multi-lobe bearing and tilting pad bearing, and more recently the foil bearing. These fluid film bearings provide progressively improved stability characteristics, at the cost of lower load carrying capacity and reduced damping at critical speeds.
The second problem with fluid film bearings is their speed dependent characteristics. The stiffness and damping properties of fluid film bearings depend on the Sommerfeld number, which is a nondimensional speed/load factor. The difficulty of determining accurate stiffness and damping properties of fluid film bearings is prevalent up to the present time, both due to the difficulty of the CFD calculations using Finite Difference and Finite Element Methods, as well as the speed dependent properties which affect the prediction of critical speeds of rotors mounted on fluid film bearings.
Large, heavy rotors have to use fluid film bearings because of the load carrying capacity. However, smaller and faster rotors are mounted on rolling element bearings. Unfortunately, rolling element bearings, do not provide any vibration control, because of their high stiffness and virtually no damping characteristics. This did not cause problems with smaller machines, such as electric motors, but with the advent of gas turbine jet engines, which necessitated the use of high speed, light rotors, it became apparent that aircraft engines need a method of vibration control. Fluid film bearings were eliminated as a possible control method in aircraft engines because of the instability mechanisms of oil whip, which would be destructive for high-speed engines.
The time was ripe in the nineteen sixties for the introduction of the squeeze film damper and soft support as a method for passive vibration control. The squeeze film damper is an oil film surrounding the outer race of a rolling element bearing which is constrained from rotation but allowed to vibrate. Thus, it can be classified as a class of fluid film bearings, without the load carrying capacity or the instability caused by rotation. The squeeze film damper allowed the designer of aircraft engines to introduce damping to the rotating machine as a method of vibration control. In addition, the introduction of the soft support allowed judicial placement of the critical speeds. Thus the combination of the squeeze film damper and soft support provided the designer with stiffness and damping to control the rotor vibration passively.
In the nineteen eighties, researchers started toying with the idea of using magnetic bearings as supports for rotating machines. This opened the door for active control of rotating machine vibration, because of the possibility of actively controlling the stiffness and damping properties of magnetic bearings through the control of the current to the bearings. In addition, it is somewhat natural to consider active control of electromagnetic systems, due to the ease of interface with control system components.
A wealth of research exists in the literature on the active control of rotating machinery using magnetic bearings. Actually, it is the inventor's personal belief that magnetic bearings, despite their various shortcomings, are probably the best method available to control rotor vibration in land based applications.
The magnetic bearings can provide continuously variable stiffness and damping properties for active vibration control, add to that the non-contact characteristics, as well as a large load carrying capacity and the possibility of using an oil free machine, and it becomes clear that magnetic bearings are probably the best choice for the support and active control of rotating machine vibrations.
However, magnetic bearings have various shortcomings. These include: the cost of magnetic bearings, which are considerably more expensive than conventional bearings; the cost of failure, which probably would mean complete replacement of the machine; the weight of the large bearings and associated controls; the sensitivity of magnetic bearings to high temperatures; the need to establish their reliability, as well as the need to establish a parallel support system, called a “catcher-bearing”, to carry the rotor in case of failure.
These shortcomings affect the application of magnetic bearings in aircraft engines, and to date, with over twenty years of aggressive research and development, no magnetic bearings have been introduced in aircraft engines. However, many rotating machines, particularly retrofit compressors, have been employed using magnetic bearings in the field and have shown considerable success.
History of Fluid Film Bearing Instability.
In an excellent paper, Y. Hori in 1959 provided a theory of oil whip, and described the history of fluid film bearing instability. According to Hori, the phenomena of oil whirl and oil whip were first reported in 1925. Although it has been three quarters of a century since the instability has been reported, yet this subject is still of current interest. G. Kirk in 2003 explained that this interest lies essentially in answering the following two questions: “Are there any possibilities that the rotor system can transgress the threshold speed? Can the rotor system operate above this threshold speed?”. These two questions are also the motivation for this work presented herein, in addition to the need to understand the parameters that influence the onset of instability.
Perhaps the interest in studying the stability of fixed geometry fluid film bearing lies in its historical significance. They allowed the development of rotating machines in the nineteenth century. Actually, in his book on the theory of lubrication, D. D. Fuller suggests that the fluid film bearing is probably the single most important element in the recent technological development, only comparable in its significance to the effect of electricity. Early fluid film bearings were designed to carry the loads, and were hailed as low-friction devices possibly capable of continuously carrying the machine. However, with the increased speed of rotating machines in the twentieth century, it became evident that the journal bearing itself can cause the problems of oil whirl and oil whip. This has caused many researchers to investigate, experimentally and theoretically, the phenomena of oil whirl and oil whip.
In his paper, Hori's main result was to explain the experimental results reported at that time. Hori reports that B. L. Newkirk and J. F. Lewis in 1956 reported experimental cases in which the rotating speed reached five or six times the first critical speed before the instability occurred, while O. Pinkus in 1953 and 1956 reported cases where whipping disappeared and resumed again, and cases of stable and unstable states separated by regions of transient whip. According to Hori, Newkirk and Pinkus experiments were contradictory in many senses; even on the effect of temperature. Newkirk and Lewis reported that hotter oil provides a greater range of stable operation, while the Pinkus experiments reported in 1956 showed that cooler oil provides a greater range of stable operation. Y. Hori in 1959 provided a theory of oil whip, trying to explain the gap between Newkirk and Pinkus.
Since then, in the sixties and seventies, significant work on alternative fluid film bearing designs to control the instability were conducted. Moreover, significant efforts went into calculating linearized bearing coefficients and in predicting rotor dynamic response.
In the eighties, renewed interest in the journal bearing instability was triggered. A. Muszynska performed extensive testing on journal bearing supported rotors. She illustrated the presence of second mode whirl. Also, in the eighties, major advances in understanding the nonlinear dynamics of journal bearings through bifurcation analysis and Hopf Bifurcation were made.